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25 views

Estimating a distribution from a dataset with multiple parameters

How would you go about solving the following problem? You're an insurance company who writes workers compensation policies. You want to build a probability distribution for the number of annual ...
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0answers
17 views

Estimating Parameters of truncated generalized pareto distribution by probability weighted moments

Is it possible to estimate parameters for a truncated Generalized Pareto Distribution (Wikipedia Article) by probability weighted moments? If not, why is that so? I am aware that it would be possible ...
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1answer
69 views

Logistic Regression - Model Does not Fit

My name is Abhi and I am fairly new to statistics. I found some sample exercises online & I am trying to solve them to get a better understanding of model development. Problem Statement Assume ...
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3answers
81 views

Issues with fitting distribution to heavy-tailed data

I am currently trying to fit distributions to some heavy tailed data-set (see the data set below) and have a hard time producing good results: ...
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1answer
32 views

Estimating a distribution based on three percentiles and a mean

I have a set of percentiles the 10-th, 50-th and 90-th. Furthermore I have the mean value. I am trying to reconstruct the underlying distribution. The question is similar to Estimating a ...
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1answer
38 views

Finding analytic form for distributions using linear regression, need ideas

I'm trying to find an analytical form to describe these probability density functions: I'm pretty new to all of this, but think I should use some linear combination of basis functions (so I can then ...
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1answer
50 views

“Better” goodness-of-fit tests than chi squared for histogram modeling?

I work on data from a mass spectrometer that produces billions upon billions of count histograms, and I need a good way to test whether these histograms are consistent with one or several model ...
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1answer
47 views

Regression model for $f(x_1, x_2) = a + b x_1\log x_2$

Which regression algorithm do I need to use to fit the coefficients of $f(x_1, x_2) = a + b x_1\log x_2$? Will linear regression with an independent variable $x_1 \log x_2$ work?
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0answers
24 views

How to find out some particular distribution given the grouped data and a polynomial fitted to the data

I have to analyse a set of grouped data.The data is divided into groups by some categories for example: BP(<=60), BP((60,80]); Pulse(<75), Pulse((75,90]) & Pulse(>90) etc having many more ...
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0answers
55 views

Fitting for a Poisson-Gaussian Mixture Distribution

First of all, I am rather new to statistics, so go easy on me. I am aware that the negative binomial distribution can be thought to arise as a result of letting the $\lambda$ parameter in a Poisson ...
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0answers
13 views

How to incorporate a noise model into a probabilistic model?

Let's say have a probabilistic model $m$ which I fit to data using maximum likelihood. Now, I would like to add a noise model $n$ which I can also fit independently using maximum likelihood. So I am ...
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0answers
33 views

Curve Fitting - Objective functions

This is more of an open ended question: I am currently doing some non-linear curve fitting of different types of curves to some noisy data (gaussian and lorentzian peaks). I use the simplest ...
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0answers
43 views

How to know one system is significantly better than another one?

I am studying lexical semantics. I have 65 pairs of synonyms with their sense relatedness. The dataset is derived from the paper: Rubenstein, Herbert, and John B. Goodenough. "Contextual correlates ...
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0answers
16 views

Finding the right parameter for a student's $t$-distribution

Suppose I have a homogeneous time series $x_n$, where the values arrive each second. For $n\ge 60$, let $\sigma_n$ be the standard deviation of the values $x_{n-59},\ldots,x_n$. Under the assumption ...
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1answer
32 views

fitted() function in R vs adding the residuals to the original data

I've found a discrepancy between the output of the fitted() function and adding the residuals to the original data set. Is the fitted() function not doing what I think it should be doing?
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2answers
55 views

How to show that there is no relationship

I have some data which I am using to show that there is no relationship between two variables. (Or only a weak one.) In a previous writeup, I included the scatterplot showing no visible relationship, ...
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1answer
28 views

Number of points crossed by their best fit line

My lab teacher asked this question in class, but i find no way to work it out. If I have $n$ points with their uncertainties, I know that they follow a linear expression and I find the best-fit line ...
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0answers
31 views

Bank loan model (spr?)

I am trying to fit a model investigating the amount of the loan (or a transformation of it) as a function of the the variables income, gender, customer and age. Fitting a standard linear regression ...
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0answers
29 views

Effective variance for two independent variables

When you're fitting a model $y=f(x)$ to data (${x_i, y_i}$) with errorbars on both the independent ($x$) and response ($y$) variables, it's standard that you can define an 'effective variance' when ...
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2answers
130 views

Fit distributions with glm

I'm trying to fit different statistical distributions (Gamma, Poisson, normal, inverse Gaussian) to my data with a glm. An example could be like this: ...
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1answer
72 views

Negative binomial distribution fit

I am trying to fit a negative binomial distribution, in R, to my over dispersed data (out of 20 ,14 samples are 0, and rest are less than 5). The mean is $-0.8$ and ...
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1answer
52 views

Fit a moving average (MA) time series model to the data (R:stats::ar equivalent)

I am looking for some tools for automatic fitting of moving average (MA) time series model to my data in R. I know R:stats::ar ...
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0answers
33 views

Mixing distributions to model parameter errors in Poisson

I'm trying to fit a complex model to count data from a detector. I have background and background+signal data. My goal is to obtain information from the signal by fitting a Poisson with $\lambda = ...
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1answer
52 views

Model fitting to data by using machine learning algorithms?

I am trying to fit an equation to data. I know the form of the equation but I need to know constants parameters in the equation. I used non-linear fitting and optimization techniques but I could not ...
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3answers
79 views

Fitting moments to a distribution

I have data on the first to fourth moments of a continuous random variable and I am trying to find what distribution best fits the data. Wikipedia has a list of about 20 distributions that could fit ...
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1answer
111 views

Digging deeper into the FitDist function

I am using the script allfitdist to find which distribution best fits my data according to the tests included (BIC, AIK etc...) - these all stem from the script ...
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0answers
38 views

Determining the uncertainty of an exponential fit

My problem should probably be built up from the beginning, so lets start there. I performed a certain experiment 25 times. Every time, the experiment consists of 5000 measurements, and each ...
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0answers
84 views

How to interpret log-likelihood outputs from MASS::fitdistr (R)

AIM: Fit the best distribution to columns in a dataset (30k records) so that I can to go on to produce test data that is in a similar distribution. WHAT I'VE DONE SO FAR: Using R, I have found and ...
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0answers
61 views

Back Transforming Rates in Poisson GLM with Box and Cox Transformation

Suppose I have fitted a Poisson GLM to model rates as follows: > fit.1=glm(response~X1+X2+ offset(log(population)),family=poisson,data=...) I can get the ...
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0answers
24 views

Confidence interval for fit to poisson count data, for beginner

I have the following graph, which I then normalise and attempt to fit to. The data is a histogram of counts at a given time. The fit then looks like: The issue is that the parameters ...
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0answers
57 views

Error bar for Poisson count data

I have a set of data, counts versus time. The whole data looks like this Here is a sample ...
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0answers
92 views

How to fit this neuron firing model with R?

I originally posted this as an answer elsewhere but in retrospect it seems more like a question: What is the sample-size range for which the median should be preferred to the mean as a measure of ...
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1answer
74 views

Fitting logistic function with pymc

I've asked this question on stackoverflow too, but no answer yet. This seems a more appropariate place to ask this question: I'm messing around with pymc to understand it a bit better. Now I am ...
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0answers
41 views

Connection between power law and Zipf's law

I am trying to better understand the connection between the power law distribution and Zipf's distribution (law). There is a neat explanation in [1]. The article suggests that as we can derivate the ...
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1answer
183 views

Which distribution fits data better?

I use fitdistr in R to select which distribution fits my data best. I tried cauchy, ...
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1answer
533 views

Fitting ARMA model with MATLAB R2012b

I want to fit an ARMA model on a time series (quarterly log returns of a 10 year bond) using MATLAB R2012b. This is part of an exercise. I have problems with the code and the interpretation of a ...
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0answers
13 views

Testing parameter estimates

If I have derived parameter estimates for a distribution for some data, do I need to conduct a significance test on these to determine how valid they are? Or is the same effect done by just performing ...
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1answer
141 views

Fitting a copula with Poisson marginals to data in R

First off, I know this is a question which requires an thorough answer, so I am coming here with a very humble attitude. I have limited knowledge about both copulas and R, so I will try to explain ...
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1answer
107 views

t-distribution parameter estimation

I know there are already several threads on this, but none seem to explicitly cover what I want. I have a set of financial data (pulled straight from Bloomberg) and am trying to fit a t-distribution ...
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0answers
83 views

Warnings in R after “fitdistr” used

I have just tried to fit a t-dist in R for some data, and did this by reading in a 21x1 csv file and converting to numeric (can show code used if you think it's important). It has produced parameters ...
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0answers
41 views

Fitting a Non-Central t-Distribution with Location and Scale Transformations

I am trying to fit a distribution function to empirical observations that have the following properties: Non-zero mean Non-unit variance Heavy tails Asymmetric about the mode I am considering ...
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1answer
103 views

Parameter fitting with STAN?

I have a model that produces data given a set of parameters. Now, given data, I'ld like to find out which parameters of the model are likely. I have an implementation in Matlab that uses Delayed ...
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1answer
81 views

Fitting distribution to spatial data

Cross posting my question from mathoverflow to find some stats specific help. I am studying a physical process generating data which projects nicely into two dimensions with non-negative values. ...
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0answers
25 views

Fitting of bivariate data to a self-defined probability density function

I have a bivariate set of data points which I want to fit to a self-defined distribution (i.e. not standard normal or chi-square or like that, a different, let's say "new" density function). I would ...
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1answer
83 views

Chi-squared Goodness of Fit - very small expected values

I am trying to calculate chi-squared value for my fitted data using: $$ \chi^2 = \sum_i^n{\frac{(y-f(x))^2}{f(x)}} $$ where $f(x)$ are theoretical values from fitted function and $y$ are ...
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2answers
90 views

Fit power law for distributions with zeroes

I am pretty new to statistics and have some data that I think may follow a power-law distribution. However, it includes zeroes. I understand that mathematically zeroes can't work, but conceptually, ...
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1answer
153 views

Why am I not able to fit a zero inflated poisson distribution?

Following what is suggested here http://stackoverflow.com/questions/7157158/fitting-a-zero-inflated-poisson-distribution-in-r ...
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0answers
110 views

Bootstrapping fits to a small sample

I have a sample of experimentally measured survival times that are quite noisy and vary stochastically. The survival probability of these events (number of events with a survival time of t or more) is ...
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2answers
86 views

Occam's razor (when is it appropriate to add another free parameter?)

So if I fit data to a function you can almost always decrease $\chi_{\nu}^2$ by adding more free parameters. However, this becomes ridiculous if you are fitting a 100-order polynomial to a straight ...
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0answers
22 views

Appropriateness of applying a fitted model to a different (but similar) set of predictor variables

I have fitted a model of current species habitat suitability as a function of mean annual temperature (MAT) and precipitation (MAP) by regressing the distribution of known occurrences of a species ...